Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations

TL;DR

This paper demonstrates that voluntary reward systems can promote the emergence and sustainability of pool punishment in large populations, helping to maintain public goods despite second-order free riders.

Contribution

It introduces the concept that reward funds can facilitate the transition from free riding to pool punishment, a novel insight into social norm evolution.

Findings

Reward funds enable pool punishment to emerge despite free riding.

Rewarding contributors to punishment promotes social norm transitions.

Reward funds diminish as pool punishment becomes self-sustaining.

Abstract

Punishment is a popular tool when governing commons in situations where free riders would otherwise take over. It is well known that sanctioning systems, such as the police and courts, are costly and thus can suffer from those who free ride on other's efforts to maintain the sanctioning systems (second-order free riders). Previous game-theory studies showed that if populations are very large, pool punishment rarely emerges in public good games, even when participation is optional, because of second-order free riders. Here we show that a matching fund for rewarding cooperation leads to the emergence of pool punishment, despite the presence of second-order free riders. We demonstrate that reward funds can pave the way for a transition from a population of free riders to a population of pool punishers. A key factor in promoting the transition is also to reward those who contribute to pool punishment, yet not abstaining from participation. Reward funds eventually vanish in raising pool punishment, which is sustainable by punishing the second-order free riders. This suggests that considering the interdependence of reward and punishment may help to better understand the origins and transitions of social norms and institutions.